Gamma分布的特征函数及点估计

Characteristic Function of Gamma Distribution and Its Point Estimation

利用特征函数及其性质 ,给出Gamma分布的数字特征的几个重要定理的证明 .同时 ,讨论了Gamma分布的参数估计问题 ,在形状参数α已知的条件下 ,给出尺度参数λ的一个渐近有效估计λ^ =(nα -1) / ∑ni=1xi,其效率en =1- 2nα .

By the characteristic function and its properties,the few important theorms about Gamma distribution's numerical charateristics such as mean,variance and moment ect.are simply proved.In addition,the problem of parameter estimation are discussed,when the shape parameter α is known,the asymptotic effective estimation to the scale parameter λ is given as λ^=(nα-1)/∑ni=1X i,and the efficiency e n is provided by e n=1-2nα.